What's the difference between a Galilean and a Keplerian Telescope?
Galilean telescopes are small and lightweight due to their rather simple optical design. They produce a bright image but offer rather narrow fields of view (about 5 degrees at 4x) and tend not to be sharp edge-to-edge. They are available as both fixed-focus and focusable versions and are usually prescribed in 1.7x and 2.2x powers though other powers are also available. Because of their small size and low weight they are convenient for binocular prescriptions.
The Galilean telescope contains a convex objective lens and a concave eyepiece lens. The telescope is short but provides a narrower field of view than Keplerian designs especially in higher powers.
Keplerian telescopes are longer and heavier as they incorporate prisms to reorient what would otherwise be an inverted image. They offer fields of view at least twice as large (about 12 degrees at 4x) as Galilean telescopes. They usually incorporate larger objective lenses to produce brighter images. All commercially available Keplerian telescopes are focusable and are most frequently prescribed in 3x, 4x, 5x and 6x powers.
The Keplerian telescope contains a convex objective lens and convex eyepiece lenses. The system is longer and requires prisms to properly orient the image. It provides a wider field of view than Galilean optical designs.
Galilean Telescope: Example of a 5 degree field of view
Keplerian Telescope: Example of a 12.5 degree field of view